Central product of D8 and Q8 | 32 (50) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (4) Subgroup rank of a group (4) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of D8 and Z8 | 32 (38) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (2) Derived length (2) Frattini length (3) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of UT(3,3) and Z9 | 81 (14) | Order of a group (81) Prime-base logarithm of order (4) Exponent of a group (9) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Fitting length (1) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (1) |

Central product of UT(3,Z) and Q | | Nilpotency class (2) Derived length (2) |

Central product of UT(3,Z) and Z identifying center with 2Z | | Nilpotency class (2) Derived length (2) Frattini length (2) Hirsch length of a polycyclic group (3) Polycyclic breadth (3) |

Dihedral group:D32 | 32 (18) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (16) Prime-base logarithm of exponent (4) Nilpotency class (4) Derived length (2) Frattini length (4) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (1) Characteristic rank of a p-group (1) |

Direct product of A4 and Z2 | 24 (13) | Order of a group (24) Exponent of a group (12) Derived length (2) Frattini length (1) Minimum size of generating set (2) Subgroup rank of a group (3) |

Direct product of D8 and V4 | 32 (46) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (4) Subgroup rank of a group (4) Rank of a p-group (4) Normal rank of a p-group (4) Characteristic rank of a p-group (3) |

Direct product of Q8 and Z2 | 16 (12) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

Direct product of prime-cube order group:U(3,3) and Z3 | 81 (12) | |

Fundamental group of Klein bottle | | |

GAPlus(1,R) | | |

General affine group of degree one | | |

General affine group:GA(1,Q) | | |

Generalized dihedral group for 2-quasicyclic group | | |

Generalized dihedral group for additive group of 2-adic integers | | |

Generalized dihedral group for direct product of Z4 and Z4 | 32 (34) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (2) |

Generalized quaternion group:Q16 | 16 (9) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (3) Derived length (2) Frattini length (3) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (1) Normal rank of a p-group (1) Characteristic rank of a p-group (1) Number of conjugacy classes (7) Number of equivalence classes under rational conjugacy (6) Number of conjugacy classes of rational elements (5) |

Infinite dihedral group | | Derived length (2) Fitting length (2) Frattini length (1) Subgroup rank of a group (2) |

M16 | 16 (6) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (2) Derived length (2) Frattini length (3) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

Nontrivial semidirect product of Z4 and Z4 | 16 (4) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) Number of subgroups (15) Number of conjugacy classes of subgroups (13) Number of conjugacy classes (10) |

Nontrivial semidirect product of Z9 and Z9 | 81 (4) | Order of a group (81) Prime-base logarithm of order (4) Exponent of a group (9) Prime-base logarithm of exponent (2) Frattini length (2) Derived length (2) Nilpotency class (2) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

Quotient of UT(3,Q) by a central Z | | Nilpotency class (2) Derived length (2) |

Restricted regular wreath product of group of prime order and quasicyclic group | | |

Semidihedral group:SD16 | 16 (8) | Underlying prime of p-group (2) Order of a group (16) Prime-base logarithm of order (4) Max-length of a group (4) Chief length (4) Composition length (4) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (3) Derived length (2) Frattini length (3) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (1) Characteristic rank of a p-group (1) Number of conjugacy classes (7) Number of equivalence classes under rational conjugacy (6) Number of conjugacy classes of rational elements (5) |

Semidihedral group:SD32 | 32 (19) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (16) Prime-base logarithm of exponent (4) Nilpotency class (4) Derived length (2) Frattini length (4) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (1) Characteristic rank of a p-group (1) |

Semidirect product of Z8 and Z4 of M-type | 32 (4) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (8) Prime-base logarithm of exponent (3) Nilpotency class (2) Derived length (2) Frattini length (3) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) |

SmallGroup(32,2) | 32 (2) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Max-length of a group (5) Chief length (5) Composition length (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Frattini length (2) Nilpotency class (2) Derived length (2) Minimum size of generating set (2) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (3) |

SmallGroup(32,24) | 32 (24) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (3) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (3) |

SmallGroup(32,27) | 32 (27) | Underlying prime of p-group (2) Order of a group (32) Prime-base logarithm of order (5) Exponent of a group (4) Prime-base logarithm of exponent (2) Nilpotency class (2) Derived length (2) Frattini length (2) Minimum size of generating set (3) Subgroup rank of a group (4) Rank of a p-group (4) Normal rank of a p-group (4) Characteristic rank of a p-group (4) |

SmallGroup(81,3) | 81 (3) | Order of a group (81) Exponent of a group (9) Frattini length (2) Fitting length (1) Derived length (2) Nilpotency class (2) Minimum size of generating set (2) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (3) Number of conjugacy classes (33) Number of subgroups (41) Number of conjugacy classes of subgroups (23) |

Sylow subgroup of holomorph of Z27 | 243 (22) | Order of a group (243) Exponent of a group (27) Nilpotency class (3) Derived length (2) Frattini length (3) Fitting length (1) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (2) Normal rank of a p-group (2) Characteristic rank of a p-group (2) Number of conjugacy classes (35) |

Sylow subgroup of holomorph of cyclic group of odd prime-cube order | | |

Unitriangular matrix group:UT(3,Q) | | Nilpotency class (2) Derived length (2) |

Unitriangular matrix group:UT(3,Z) | | Nilpotency class (2) Derived length (2) Frattini length (2) Hirsch length of a polycyclic group (3) Polycyclic breadth (3) |

Wreath product of Z3 and Z3 | 81 (7) | Order of a group (81) Exponent of a group (9) Nilpotency class (3) Derived length (2) Fitting length (1) Frattini length (2) Minimum size of generating set (2) Subgroup rank of a group (2) Rank of a p-group (3) Normal rank of a p-group (3) Characteristic rank of a p-group (3) |